Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with Ih Symmetry
(Uniform #23) (Dodecahedron)
(2 of 2)
Vertices:  20  (20[3])
Faces:12  (regular pentagons)
Edges:30  (all same length)
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle:  acos(−sqrt(5)/5)    ≈116.565051177 degrees
Dual Solid:  Icosahedron
(values below based on midscribed radius = 1)
Edge Length:  3−sqrt(5)    ≈0.76393202250021030359
Circumscribed Radius:  (sqrt(15)−sqrt(3))/2    ≈1.0704662693192697958
Midscribed Radius:  1
Inscribed Radius:  sqrt(10*(5+sqrt(5)))/10    ≈0.85065080835203993218
Volume:2*(3*sqrt(5)−5)    ≈3.41640786499873817846